1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: More Cantor set fun

  1. Nov 30, 2011 #1
    1. The problem statement, all variables and given/known data

    I have two numbers: 509/729 and 511/729. I want to determine if they are in the Cantor set.

    3. The attempt at a solution

    I have:

    509/729 in base 3 is: 0.200212

    So this is not part of the cantor set because it can't be expanded in base 3 using only 0 and 2.


    511/729 in base 3 is: 0.200221

    For this one, am I correct in saying that 0.200221 = 0.200220222...

    So, it can be expanded using only 0 and 2, and so is part of the cantor set?
  2. jcsd
  3. Nov 30, 2011 #2
    Indeed, both look good to me!!
  4. Nov 30, 2011 #3


    User Avatar
    Science Advisor

    Since we form the Cantor set by removing open intervals, the endpoins of those intervals remain in the Cantor set. .02002213 is such an endpoint.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook